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# Working with Algebraic Expressions Practice Questions

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Updated on Sep 23, 2011

## Introduction

This question set contains 25 algebraic expressions; each can contain up to five variables. Remember that a variable is just a letter that represents a number in a mathematical expression. When given numerical values for the variables, you can turn an algebraic expression into a numerical one.

As you work through the problems in this study guide, you are to substitute the assigned values for the variables into the expression and evaluate the expression. You will be evaluating expressions very much like the previous numerical expressions. The answer section contains complete explanations of how to go about evaluating the expressions. Work on developing a similar style throughout, and you will have one sure way of solving these kinds of problems. As you become more familiar and comfortable with the look and feel of these expressions, you will begin to find your own shortcuts.

Read through the Tips for Working with Algebraic Expressions before you begin to solve the problems in this section.

## Tips for Working with Algebraic Expressions

• Substitute assigned values for the variables into the expression.
• Use PEMDAS to perform operations in the proper order.

## Practice Questions

Evaluate the following algebraic expressions when

a = 3

b = 5

x = 6

y =

z = 8

1. 4a + z
2. 3x ÷ z
3. 2axz
4. 5ab + xy
5. 4b2az
6. 7x ÷ 2yz
7. bx + z ÷ y
8. 6y – 2ab
9. a(b + z)2
10. 2(a2 + 2y) ÷ b
11. a3 + 24y – 3b
12. 2xb + az
13. 5z2 – 2z + 2
14. 5xy ÷ 2b
15. 7x + z
16. 2b2 ÷ y
17. bx(z + 3)
18. 6y(z ÷ y) + 3ab
19. 2bx ÷ (zb)
20. 12ab ÷ y
21. y{( – 3) – 4a}
22. 10b3 – 4b2
23. 8y(a3 – 2y)
24. z2 – 4a2y
25. 3x2b(5a – 3b)

Numerical expressions in parentheses like this [ ] are operations performed on only part of the original expression. The operations performed within these symbols are intended to show how to evaluate the various terms that make up the entire expression.

Expressions with parentheses that look like this ( ) contain either numerical substitutions or expressions that are part of a numerical expression. Once a single number appears within these parentheses, the parentheses are no longer needed and need not be used the next time the entire expression is written.

When two pair of parentheses appear side by side like this ( )( ), it means that the expressions within are to be multiplied.

Sometimes parentheses appear within other parentheses in numerical or algebraic expressions. Regardless of what symbol is used, ( ), { }, or [ ], perform operations in the innermost parentheses first and work outward.

Underlined expressions show the original algebraic expression as an equation with the expression equal to its simplified result.

a = 3

b = 5

x = 6

y =

z = 8

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